2. Consider the following market for used cars. The set of possible quality types is given by the interval (0, s), with each type having the same probability. Any car's true quality is known only by its seller. Each seller values their car at 015, yet may choose instead to sell the car for p. Buyers expect to receive 02u -p if they purchase, and 0 if they do not purchase, where u is the buyer's expectation of quality. a) Under what circumstances should trade take place? Explain. b) Determine, given any p, a buyer's anticipation of quality, u. c) Given your answer to b), determine the condition which describes a buyer's purchase decision given any price. Under what circumstances can market trade occur?

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter7: Uncertainty
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Problem 7.5P
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2. Consider the following market for used cars. The set of possible quality types is given by
the interval (0, 3), with each type having the same probability. Any car's true quality is known
only by its seller. Each seller values their car at 01s, yet may choose instead to sell the car for
p. Buyers expect to receive 62u – p if they purchase, and 0 if they do not purchase, where u is
the buyer's expectation of quality.
a) Under what circumstances should trade take place? Explain.
b) Determine, given any p, a buyer's anticipation of quality, .
c) Given your answer to b), determine the condition which describes a buyer's purchase decision
given any price. Under what circumstances can market trade occur?
d) Assuming trade can arise, is there a welfare maximizing price?
e) Explain the potential for market failure in this model - how can it be that there is no price
such that trade can take place?
Transcribed Image Text:2. Consider the following market for used cars. The set of possible quality types is given by the interval (0, 3), with each type having the same probability. Any car's true quality is known only by its seller. Each seller values their car at 01s, yet may choose instead to sell the car for p. Buyers expect to receive 62u – p if they purchase, and 0 if they do not purchase, where u is the buyer's expectation of quality. a) Under what circumstances should trade take place? Explain. b) Determine, given any p, a buyer's anticipation of quality, . c) Given your answer to b), determine the condition which describes a buyer's purchase decision given any price. Under what circumstances can market trade occur? d) Assuming trade can arise, is there a welfare maximizing price? e) Explain the potential for market failure in this model - how can it be that there is no price such that trade can take place?
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